David K.H. Begg, Gianluigi Vernasca-Economics-McGraw Hill Higher Education (2011)

5.3 Adjustment to price changes
This hypothetical income that we can give to our consumer in order to make her as well off as before a
price change is what economists call compensating variation.4
If confronted with the hypothetical budget line HH, the consumer would choose bundle D. Why do we
need to do all of this? Because we can now decompose graphically the movement from C to E into two
different steps: the movement from C to D and then from D to E.
The movement from C to D depends only on the price change, and we call that the substitution effect. The
movement from D to E depends only on the fact that the real income has changed, and we call that the
income effect.
The move from C to D is the pure substitution effect that is the adjustment of demand to relative prices
when income is adjusted to maintain the old standard of living in the face of the new higher prices. The
substitution effect of an increase in the price of meals unambiguously reduces the quantity of meals demanded.
This result is perfectly general. 5 As meals become relatively more expensive, the consumer switches towards
films, which have become relatively cheaper. Therefore, in moving from C to D, the quantity demanded of
meals decreases while the quantity demanded of films increases. In general, the substitution effect is always
negative for the good whose price has changed. This means that the consumer will always substitute the
good that is now relatively expensive with the good that is now relatively cheap.
The income effect
To isolate the effect of the reduction in real income, holding relative prices constant, consider now the
parallel shift in the budget line from the hypothetical position HH to the actual new position AF'. The
consumer moves from D to E. When both goods are normal goods, a reduction in real income will reduce
the quantity demanded of both goods. This is the case considered in Figure 5.13, where E lies to the south-west
of D. From Figure 5.13 we see that, for meals, the income and substitution effects go in the same direction,
meaning they reinforce each other in reducing the quantity consumed of meals. This is a general feature of
normal goods. When the price of a normal good changes, the substitution and income effects for that good
reinforce each other.
Income and substitution effects in practice: the
effects of petrol prices on grocery expenditure
Many consumers use cars to go shopping at grocery shops. Recent research tried to understand how changes in
the price of petrol can affect the consumption of grocery products for consumers in California. In order to do that,
the researchers used data from the Consumer Expenditure Survey and from detailed scanner data from grocery
shops about food products. The research explored the following: suppose that consumers can choose between
different bundles containing the following two goods: food away from home (like eating out in a restaurant) and
food at home (like grocery shop food). If the price of petrol increases, eating out and going to the grocery shop
using a car become more expensive. How do petrol price increases affect expenditure on those two goods?
The researchers found that, if the price of petrol doubles, the expenditure (and so the consumption) of food
away from home decreases by 56 per cent. On the other hand, when the petrol price doubles, the expenditure
on grocery food increases by around 19 per cent. This means that, when petrol price increases, food away
Q
4 In the case of a decrease in the price of meals, the compensating variation would be the amount of income that we need to take
away from our consumer in order for her to be as well off as before.
5 With only two goods, substitution away from meals must imply substitution towards films. However, when there are more than
two goods, we cannot be sure that the substitution effects will tend to increase the quantity demanded for all other goods. We discuss
this shortly in Section 5.5.
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